Green functions of electrons in monolayer and bilayer graphene in a magnetic field

Abstract

Closed expressions for the Green functions of the stationary two-dimensional two-component Schrodinger equation for an electron moving in monolayer and bilayer graphene in the presence of a magnetic field are obtained in terms of the Whittaker functions.

arXiv comment7 pages, 2 figures, 2 exact results, published verion

References in corpus (6)

• Landau level degeneracy and quantum Hall effect in a graphite bilayer
• Magnetic field driven metal-insulator phase transition in planar systems
• AC conductivity of graphene: from tight-binding model to 2+1-dimensional quantum electrodynamics
• Dynamical Flavor Symmetry Breaking by a Magnetic Field in $2+1$ Dimensions
• High magnetic field theory for the local density of states in graphene with smooth arbitrary potential landscapes
• The Electron Propagator in External Electromagnetic Fields in Lower Dimensions

Cited by in corpus (8)

• Magnetic field driven instability of charged center in graphene
• Valley properties of doped graphene in a magnetic field
• Statistical repulsion/attraction of electrons in graphene in a magnetic field
• Theory of Friedel oscillations in monolayer graphene and group-VI dichalcogenides in a magnetic field
• Abelian Chern-Simons Theory for the Fractional Quantum Hall Effect in Graphene
• Partial preservation of chiral symmetry and colossal magnetoresistance in adatom doped graphene
• Interplay of resonant states and Landau levels in functionalized graphene
• Part 1. Infinite series and logarithmic integrals associated to differentiation with respect to parameters of the Whittaker ${\mathrm{M}}_{\kappa ,\mu }\left(x\right)$ function